Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods
  • G06N3/084—Backpropagation, e.g. using gradient descent
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N20/00—Machine learning
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/004—Artificial life, i.e. computing arrangements simulating life
  • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/044—Recurrent networks, e.g. Hopfield networks
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/045—Combinations of networks

Definitions

• This specification relates to reinforcement learning.
• an agent interacts with an environment by performing actions that are selected by the reinforcement learning system in response to receiving observations that characterize the current state of the environment.
• Some reinforcement learning systems select the action to be performed by the agent in response to receiving a given observation in accordance with an output of a neural network.
• Neural networks are machine learning models that employ one or more layers of nonlinear units to predict an output for a received input.
• Some neural networks are deep neural networks that include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as input to the next layer in the network, i.e., the next hidden layer or the output layer.
• Each layer of the network generates an output from a received input in accordance with current values of a respective set of parameters.
• This specification describes a reinforcement learning system implemented as computer programs on one or more computers in one or more locations that selects actions to be performed by an agent interacting with an environment.
• the system uses an action selection policy neural network in selecting actions to be performed in response to observations of the environment.
• the system trams (i) one or more auxiliary control neural networks, (ii) a reward prediction neural network, or both, that receive as inputs respective intermediate outputs of the action selection policy neural network.
• one innovative aspect may be embodied in a method for training a reinforcement learning system, where the method includes: training an action selection policy neural network using a first reinforcement learning technique, wherein the action selection policy neural network has a plurality of action selection policy network parameters and is used in selecting actions to be performed by an agent interacting with an environment, in particular in performing a main task.
• the action selection policy neural network may be configured to receive an input comprising an observation input and to process the input in accordance with the network parameters to generate an action selection policy output, and wherein training the action selection policy neural network comprises adjusting values of the action selection policy network parameters.
• the method may comprise, during the training of the action selection neural network using the first reinforcement learning technique: training each of one or more auxiliary control neural networks on interactions of the agent with the environment during the training of the action selection neural network, wherein each of the auxiliary control neural networks has respective auxiliary control parameters and corresponds to a respective auxiliary control task and is configured to: receive a respective intermediate output generated by the action selection policy neural network, and generate a policy output for the corresponding auxiliary control task in accordance with the respective auxiliary control task parameters of the auxiliary control neural network; and wherein training each of the auxiliary control neural networks comprises:
• the action selection policy output may define an action to be performed by the agent in the environment; as described later, the agent may be a robotic agent.
• an auxiliary control neural network may comprise one or more neural network layers coupled to one or more hidden layers of the action selection policy neural network, that is the intermediate output may comprise an output from these one or more hidden layers.
• training the auxiliary control neural network may also involve training part of the action selection policy- neural network, more specifically part of this network between the input and the intermediate layer.
• parameters e.g.
• weights) of the action selection policy neural network are trained by training of the action selection policy neural network, and some of these parameters are also trained by training the auxiliary control neural network(s), more specifically by backpropagatmg gradients from the auxiliary control neural network(s) into the action selection policy neural network via the intermediate output.
• the gradients may be gradients of a policy loss function for an auxiliary control task with respect to the parameters.
• the policy- output from an auxiliary control neural network may be used to compute a loss function for such backpropagation; the particular loss function depends on the auxiliary control task(s) selected; there are many such tasks which may be implemented. Very similar considerations apply for an auxiliary reward prediction neural network; in tins case the gradients may he determined from a reward prediction loss function.
• training each of the auxiliary control neural networks comprises: receiving auxiliary task rewards that are specific to the corresponding auxiliary control task in response to the interactions of the agent with the environment; and training the auxiliary control neural networks to maximize an expected task reward, more particularly an expected long-term time-discounted auxiliary task reward, for the corresponding auxiliary control task, in some cases but not essentially using a respective second reinforcement learning technique.
• the first reinforcement learning technique may be an on-policy technique and the second reinforcement learning technique may be an off-policy technique, and/or the second reinforcement learning technique may be simpler than the first, for efficiency.
• an expected long-term time-discounted auxiliary task reward may comprise an expected «-step return, more particularly a return expected after n time (action) steps actions where rewards later in time are given a reduced weighting.
• training the auxiliary control neural networks to maximize an expected long-term time-discounted auxiliary task reward for the corresponding auxiliary control task using a respective second reinforcement learning technique comprises backpropagating gradients computed, in some cases using the respective second reinforcement learning technique, into the action selection policy neural network to adjust the values of the action selection policy parameters.
• the one or more auxiliary control neural networks comprise a pixel control neural network that corresponds to a pixel control task for an observation which includes an image.
• the pixel control task may attempt to maximize, for each of one or more regions of each observation image, a maximal change in the values of pixels in the region.
• the respective reward for each of the one or more regions may be derived from a change in the pixels in the region from the observation image to a next observation image received as a result of the agent performing an action in response to the observation image.
• the pixel control neural network, and part of the action selection policy neural network may together learn to control aspects of the environment affecting the visual input, and the representations learned in the action selection policy neural network may then be useful in learning to perform the main task.
• the pixel control neural network is configured to, for a received observation image: receive the respective intermediate output for the pixel control neural network; and process the respective intermediate output to generate, for each of the one or more regions and for each of a plurality of possible actions to be performed by the agent, an estimate of a change, more particularly an estimate of the long-term time-discounted change, in the pixels in the region if the agent performs the possible action in response to the received observation image.
• the long-term time-discounted change in the pixels may comprise may comprise a change expected after n time (action) steps actions where changes later in time are given a reduced weighting.
• the pixel control neural network may comprise a
• the deconvolutional neural network may be used to determine a set of spatially mapped auxiliary reward function values, such as action-value function values, which may be used to train the pixel control neural network.
• the action selection policy neural network comprises one or more convolutional neural followed by one or more recurrent neural network layers
• the pixel control neural network may be coupled to an output of one of the one or more recurrent neural network layers.
• the auxiliary control neural networks comprise a feature control neural network that corresponds to a feature control task that attempts to maximize activations generated by one or more units in a particular hidden layer of the action selection policy neural network (winch may involve use of a corresponding target network so that the features change less frequently).
• the respective reward for each of the one or more units may be derived from a change in the activations of the unit from activations generated during processing the observation image to activations generated during processing of a next observation image received as a result of the agent performing an action in response to the observation image.
• the feature control task may be thought of as similar to a pixel control task but on higher level visual features.
• the feature control neural network is configured to, for a received observation image: receive the respective intermediate output for the feature control neural network; and process the respective intermediate output to generate, for each of the one or more units and for each of a plurality of possible actions to be performed by the agent, an estimate of the long-term time-discounted change in the activations generated by the unit if the agent performs the possible action in response to the received observation image.
• another innovative aspect may be embodied in a method for training a reinforcement learning system, where the method includes: training an action selection policy neural network using a first reinforcement learning technique, wherein the action selection policy neural network has a plurality of network parameters and is used in selecting actions to be performed by an agent interacting with an environment, wherein the action selection policy neural network is configured to receive an input comprising an observation input and to process the input in accordance with the network parameters to generate an action selection policy output, and wherein training the action selection policy neural network comprises adjusting values of the action selection policy network parameters; during the training of the action selection neural network using the first reinforcement learning technique: training a reward prediction neural network on interactions of the agent with the environment during the training of the action selection neural network, wherein the reward prediction neural network has reward prediction parameters and is configured to: receive one or more intermediate outputs generated by the action selection policy neural network that characterize a sequence of observation images received as a result of the interactions of the agent with the environment, and process the one or more intermediate outputs in accordance with the reward prediction parameters to
• training the reward prediction neural network comprises: receiving an actual reward received with the next or a subsequent observation image; and training the immediate reward neural network to decrease a loss between the actual reward and the estimated reward, more particularly the value of a loss function dependent on a difference between the actual reward and the estimated reward.
• training the reward prediction neural network may comprise sampling from sequences of observations stored in an experience replay memory, in particular so as to over-represent rewarding sequences/events, which can be advantageous when rewards in the environment are sparse.
• training the immediate reward neural network to decrease a loss between the actual reward and the estimated reward comprises: backpropagatmg gradients computed into the action selection policy neural network to adjust the values of the action selection policy parameters.
• the action selection policy neural network comprises: a convolutional encoder neural network that generates an encoded representation of the input, an intermediate neural network that processes the encoded representation of the input to generate an intermediate representation; and an output neural network that processes the intermediate representation to generate the action selection output.
• the intermediate neural network is a recurrent neural network and the one or more intermediate outputs generated by the action selection policy neural network that characterize the sequence of observation images are the intermediate representation for the last observation image in the sequence.
• the one or more intermediate outputs generated by the action selection policy neural network that characterize the sequence of observation images are the encoded representations for the observation images in the sequence.
• training the reward prediction neural network comprises sampling sequences of observations from a replay memory.
• sampling sequences of observations comprises: sampling sequences for which the actual reward received with the observation following the last observation in the sequence is non-zero with a higher probability than sequences for which the actual reward received with the observation following the last observation in the sequence is zero.
• the first reinforcement learning technique is an actor-critic reinforcement learning technique
• the action selection policy output comprises value estimates and Q-values.
• the value estimates may define the value or expected return from a state; the Q-vaiues may define the expected return for a particular action in the state, and may be implicit in, say, an advantage value defining the advantage of the action over the baseline value estimate.
• the method may then further comprise resampling recent sequences from the replay memory; and performing extra value function regression on the value estimates for the observation images in the resampled recent sequences.
• the extra value function regression may comprise additional training using the sequences from the replay memory; where an n-step return is computed the method may further randomly vary n. This can help to exploit benefits of the reward prediction task.
• aspects and implementations may be implemented by appropriate computer programs which may be carried on appropriate carrier media which may be tangible carrier media (e.g. disks) or intangible carrier media (e.g. communication signals).
• appropriate carrier media may be tangible carrier media (e.g. disks) or intangible carrier media (e.g. communication signals).
• aspects may also be implemented using suitable apparatus which may take the form of programmable computers running computer programs.
• auxiliary control neural networks or a reward prediction neural network or both can be implemented so as to realize one or more of the following advantages.
• the reinforcement learning system described in this specification can augment the feedback signals received during the training of the action selection policy neural network to improve training.
• training the auxiliary control neural networks or reward prediction neural network tunes the values of the set of parameters of the action selection policy neural network, causing them to generate more useful representations of observed data and ultimately determine more effective policy outputs to maximize cumulative extrinsic reward.
• training the reward prediction neural network tunes the values of the set of parameters of the action selection policy neural network to recognize observations that lead to receiving a high reward at a subsequent time step, and thereby allow the action selection policy neural network to determine more effective policy outputs to maximize the expected long- term time-discounted extrinsic reward, even when extrinsic rewards are only rarely non-zero.
• training reinforcement learning systems by conventional methods is slow when the training is based only on extrinsic rewards that are rarely non-zero.
• training the auxiliary control neural networks or reward prediction neural network causes the action selection policy neural network to generate representations that are closely matched with the agent's long-term goals, unlike conventional reinforcement learning systems that include unsupervised training that is generic and not closely matched with the agent's long-term goals.
• the reinforcement learning system described in tins specification trains the action selection policy neural network faster than conventional reinforcement learning systems.
• the reinforcement learning system described in this specification allows more efficient use of computational resources in training. Moreover, the reinforcement learning system described in this specification achieves superior performance to conventional reinforcement learning systems, for example by receiving more cumulative extrinsic reward.
• FIG. 1 A shows an example reinforcement learning system.
• FIG. IB shows an example implementation of a reinforcement learning system.
• FIG. 2 is a flow diagram of an example process for training the action selection policy neural network by training an auxiliary control neural network.
• FIG. 3 is a flow diagram of an example process for training the action selection policy neural network by training a reward prediction neural network.
• FIG. 1 A shows an example reinforcement learning system 100.
• the reinforcement learning system 100 is an example of a system implemented as computer programs on one or more computers in one or more locations in which the systems, components, and techniques described below are implemented.
• the reinforcement learning system 100 selects actions 110 to be performed by an agent 108 interacting with an environment 102 at each of multiple time steps.
• the system 100 receives data characterizing the current state of the environment 102, e.g., an image of the environment, and selects an action 110 to be performed by the agent 108 in response to the received data.
• Data characterizing a state of the environment 102 will be referred to in this specification as an observation 104.
• the environment 102 is a simulated environment and the agent 108 is implemented as one or more computer programs interacting with the simulated environment.
• the simulated environment may be a video game and the agent may be a simulated user playing the video game.
• the simulated environment may be a motion simulation environment, e.g., a driving simulation or a flight simulation, and the agent is a simulated vehicle navigating through the motion simulation environment.
• the actions may be control inputs to control the simulated user or simulated vehicle.
• the environment 102 is a real- world environment and the agent 110 is a mechanical agent interacting with the real- world environment.
• the agent may be a robot interacting with the environment to accomplish a specific task.
• the agent may be an autonomous or semi-autonomous vehicle navigating through the environment.
• the actions may be control inputs to control the robot or the autonomous vehicle.
• the observations 104 may be generated by or derived from sensors of the agent 108.
• the observations 104 may be captured by a camera of the agent 108.
• the observations 04 may be derived from data captured from a laser sensor of the agent 108.
• the observations may be hyperspectral images captured by a hyperspectral sensor of the agent 108.
• the system 100 uses an action selection policy neural network 1 12 in selecting actions to be performed by the agent 108 in response to observations 104 at each time step.
• the action selection policy neural network 112 is configured to receive an observation 104 as input and to process the input in accordance with a set of parameters, referred to in this specification as action selection policy neural network parameters, to generate a policy output that the system 100 uses to determine an action 1 10 to be performed by the agent 108 at the time step.
• the policy output may be a probability distribution over the set of possible actions.
• the policy output may be a Q- alue that is an estimate of the long- term time-discounted reward that would be recei ved if the agent 108 performs a particular action in response to the observation.
• the policy output may identify a particular action that is predicted to yield the highest long-term time-discounted reward if performed by the agent in response to the observation.
• the action selection policy neural network 112 includes a convolutional encoder neural network that generates an encoded representation of the input observation, an intermediate neural network that processes the encoded representation of the input observation to generate an intermediate representation, and an output neural network that processes the intermediate representation to generate the policy output.
• the system 100 receives a reward 106 based on the current state of the environment 102 and the action 110 of the agent 108 at the time step.
• the system 100 trains the action selection policy neural network 112 to generate policy outputs that maximize the expected long-term time-discounted reward received by the system 100, by using a
• the system 100 stores the experience tuple for the time step in a replay memory 1 14, where in this specification the term experience tuple refers to the observation 104 at the time step, the action 110 of the agent at the time step, the reward 106 received at the time step, and the observation of the next time step.
• the system 100 trains the action selection policy neural network 112 using an on-policy reinforcement learning technique and trains the action selection policy neural network 112 based on experience tuples as they are generated.
• An example method for on-policy reinforcement learning is described in Volodymyr Mnih et. al., "Asynchronous methods for deep reinforcement learning," Proceedings of the 33 rd International Conference on Machine Learning, 2016. Another example method for on-policy reinforcement learning is a policy gradient method.
• the system 100 trains the action selection policy neural network 112 using an off-policy reinforcement learning technique, for example one-step or n-step Q-learning, based on experience tuples as they are generated or that a sampling engine 116 samples from the replay memory 114.
• An example of an action selection policy neural network 112 is described in Volodymyr Mnih et. al., "Asynchronous methods for deep reinforcement learning," Proceedings of the 33 rd International Conference on Machine Learning, 2016.
• Other examples of action selection policy neural network 112 include DQN (Deep Q-Network), DDPG (Deep Deterministic Policy Gradient), and TRPQ (Trust Region Policy Optimization) networks.
• the system 100 may train the action selection policy neural network 1 12 by additionally training one or more auxiliary control neural networks, e.g. a pixel control neural network 118, or a feature control neural network 120, or both.
• Training the auxiliary control neural networks tunes the values of the set of parameters of the action selection policy neural network 1 12, causing the action selecting policy neural network 112 to generate more useful representations of observations 104 that are closely matched with the long-term goals of the agent 110 and thereby determine more effective policy outputs to maximize the expected long-term time-discounted reward, even when non-zero rewards 106 are only rarely received.
• Each auxiliaiy control neural network has a respective set of parameters, referred to in this specification as auxiliary control neural network parameters, and receives as input respective intermediate outputs of the action selection policy neural network 112 when processing a given observation 104. Since each auxiliaiy control neural network receives as input a respective intermediate output of the action selection policy neural network 1 2, each auxiliaiy control neural network may be considered as sharing parameters with the action selection policy neural network 112.
• An intermediate output of the action selection policy neural network 112 is a set of activations generated at one or more units of one or more hidden layers of the action selection policy neural network 1 12 in response to processing the given observation as input.
• the intermediate neural network of the action selection policy neural network 112 is a recurrent neural network and the intermediate output corresponding to a respective auxiliaiy control neural network is the intermediate representation generated by the recurrent neural network for the given observation.
• the intermediate output corresponding to the respective auxiliary control neural network is the encoded representation generated by the convolutionai encoder neural network of the action selection policy neural network 112 for the given observation.
• Each of the auxiliary control neural networks is associated with one or more respecti ve auxiliary task rewards.
• the auxiliary task rewards of the pixel control neural network 118 are derived from changes in the pixels in one or more regions from a given observation image 104 to a next observation image received as a result of the agent 110 performing an action 110 in response to the given observation 104.
• the auxiliary task rewards of the feature control neural network 120 are derived from changes in the activations generated by one or more units in a particular hidden layer of the action selection policy neural network 112 between processing a given observation 104 and processing of a next observation received as a result of the agent 108 performing an action 110 m response to the given observation.
• Each auxiliary control neural network generates an auxiliary control policy output for each associated auxiliary task reward.
• the sy stem 100 trains each of the auxiliary control neural networks to generate auxiliary control policy outputs that maximize the expected long-term time- discounted values of the corresponding auxiliary task rewards that would be achieved by selecting the actions of the agent based on the auxiliary control policy outputs.
• the system 100 trains each auxiliary control neural network 112 using a reinforcement learning technique.
• the system 100 may tram the auxiliary control neural network 112 online, based on experience tuples as they are generated, or the system 100 may train the auxiliary control neural network 112 based on experience tuples that were generated at previous time steps that a sampling engine 116 samples from the replay memory 114.
• the reinforcement learning technique may be an off-policy reinforcement learning technique, such as one-step or «-step Q- 1 earning, or the reinforcement learning technique may be an on-policy reinforcement learning technique, such as a reinforcement learning technique that estimates value functions for each auxiliary task reward.
• the system 100 backpropagat.es gradients that the system 100 determines according to the reinforcement learning technique to adjust the values of the set of parameters of the auxiliary control neural network, and to adjust the values of some of the set of parameters of the action selection policy neural network 112.
• the system adjusts the parameters of the action selection policy neural network corresponding to (i) the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network 112 that the system 100 provides as input to the auxiliary control neural network, and (ii) units that feedforward into the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network 112 that the system 100 provides as input to the auxiliary control neural network.
• a first unit is said to feed-forward into a second unit if the output of the first unit is either directly or indirectly provided as an input to the second unit.
• the system 100 may train the action selection policy neural network 1 12 by additionally training a reward prediction neural network 122.
• Training the reward prediction neural network 122 tunes the values of the set of parameters of the action selection policy neural network 112 to recognize observations 104 that lead to receiving a high reward 106 at a subsequent time step, and thereby allo ws the action selection policy neural network 112 to determine more effective policy outputs to maximize the expected long-term time-discounted reward, even when non-zero rewards 106 are only rarely observed.
• the reward prediction neural network 122 has a set of parameters, referred to in this specification as reward prediction neural network parameters, and is configured to receive as input one or more intermediate outputs generated by the action selection policy neural network 112 that characterize a sequence of observations received as a result of the interactions of the agent 08 with the environment 102. Since the reward prediction neural network 122 receives as input one or more intermediate outputs generated by the action selection policy neural network 112, the reward prediction neural network 122 may be considered as sharing parameters with the action selection policy neural network 1 12.
• the intermediate neural network of the action selection policy neural network 1 12 is a recurrent neural network and the one or more intermediate outputs generated by the action selection policy neural network 1 12 that characterize the sequence of observations are the intermediate representation generated by the recurrent neural network for the last observation in the sequence.
• the one or more intermediate outputs generated by the action selection policy neural network 112 that characterize the sequence of observations are the encoded representations of the action selection policy neural network 112 for the observations in the sequence.
• the action selection policy neural network 112 includes a convolutional encoder neural network this may encode each state of a sequence of states from the replay memory .
• the reward prediction neural network 122 processes the one or more intermediate outputs in accordance with the set of reward prediction neural network parameters to generate a predicted reward that is an estimate of an actual reward that will be received with a next observation that follows the last observation in the sequence.
• the system 100 trams the reward prediction neural network 122 to generate a predicted reward that minimizes a reward prediction loss.
• the reward prediction loss is a mean-squared error loss between the predicted reward that is received w th a next observation that follows the last observation in a sequence and the actual reward that is received with the next observation that follows the last observation in the sequence.
• the reward prediction loss is a multi-class cross-entropy classification loss, where the three classes are zero reward, positive reward, and negative reward.
• the system 100 backpropagates gradients to adjust the values of the set of parameters of the reward prediction neural network 122, and to adjust the values of some of the set of parameters of the action selection policy neural network 112, to minimize the reward prediction loss.
• the system 100 trains the reward prediction neural network 122 based on sequences of experience tuples that were generated at previous time steps that the sampling engine 16 samples from the replay memory 114.
• the sampling engine 116 samples sequences of experience tuples from the replay memory 1 14 where sequences for which the actual reward received with the observation following the last observation in the sequence is non-zero are sampled with a higher probability than sequences for which the actual reward received with the observation following the last observation in the sequence is zero.
• Biased sampling of experience tuple sequences from the replay memory 114 improves the training of the reward prediction neural network 122, and by extension the action selection policy neural network 112, particularly when non-zero rewards 106 are rarely received.
• the system 100 augments on-policy reinforcement learning to tram the action selection policy neural network 112 by additional off-policy reinforcement learning, where the off-policy reinforcement learning exploits newly discovered features of the action selection policy neural network 1 12 shaped by the system 100 training the reward prediction neural network 122.
• the reinforcement learning technique that the sy stem 100 uses to train the action selection policy neural network 1 12 may be an actor-critic reinforcement learning technique, where the policy output includes value estimates and Q- values.
• the system 100 trams the action selection policy neural network 112 using on-policy training based on experience tuples as they are generated, and performs additional off-policy reinforcement learning by performing extra value function regression on the value estimates for observations in sequences sampled by the sampling engine 116 from the replay memory 114.
• FIG. IB shows an example implementation of the system 100.
• the action selection policy neural network (a) is a convolutional long short-term memory (LSTM) network trained on-policy with the A3C loss described in Volodymyr Mnih et. al.,
• the auxiliary control neural network (b) is a pixel control neural network generating Q-value policy outputs based on experiences sampled from a replay buffer.
• the reward prediction neural network (c) generates reward predictions based on experiences sampled from the replay buffer, where r T represents the predicted reward at time step ⁇ , and skewed sampling refers to sampling sequences of experience tuples from the replay memory where sequences for which the actual reward received with the observation following the last observation in the sequence is non-zero are sampled with a higher probability than sequences for which the actual reward received with the observation following the last observation in the sequence is zero.
• the value function replay (d) indicates further reinforcement learning of the action selection policy neural network based on experiences sampled from the replay buffer.
• FIG. 2 is a flow diagram of an example process 200 for training the action selection policy neural network by training an auxiliary control neural network.
• the process 200 will be described as being performed by a system of one or more computers located in one or more locations.
• a reinforcement learning system e.g., the reinforcement learning sy stem 100 of FIG. 1, appropriately programmed in accordance with this specification, can perform the process 200.
• the system obtains an experience tuple for a time step, either as it is generated or from the replay memory, where the experience tuple includes the observation at the time step, the action of the agent at the time step, the reward received at the time step, and the observation of the next time step (step 201).
• the system provides the observation at the time step as input to the action selection policy neural network, generates an intermediate output of the action selection policy neural network corresponding to the auxiliary control neural network, and provides the intermediate output as input to the auxiliary control neural network (step 202).
• the intermediate neural network of the action selection policy neural network is a recurrent neural network and the intermediate output corresponding to the auxiliary control neural network is the intermediate representation generated by the recurrent neural network for the observation at the time step.
• the intermediate output corresponding to the auxiliary control neural network is the encoded representation generated by the convolutional encoder neural network of the action selection policy neural network for the observation at the time step.
• the system determines the auxiliary task rewards at the time step (step 203).
• the auxiliary control neural network is a pixel control neural network
• the observations are images
• the pixel control neural network is associated with an auxiliary task reward for each of one or more regions of the observation.
• the system derives the respective auxiliary task reward for each of the one or more regions from a change in the intensities of the pixels in the region from the observation image at the time step to the observation image at the next time step.
• the system may determine the change in the intensities of the pixels in a region from the observation image at the time step to the observation image at the next time step by computing the change of the average intensity of the pixels in the region.
• the system may determine the change in the intensities of the pixels in a region from the observation image at the time step to the observation image at the next time step as a sum of the squared differences in the intensities of the individual pixels in the region.
• the system may determine the one or more regions of the observation image by dividing the observation image into regions delineated by an n x n non-overlapping grid placed over the observation image.
• the pixel control neural network is a deconvolutional neural network.
• the auxiliary control neural network is a feature control neural network
• the feature control neural network is associated with an auxiliary task reward for each of one or more sets of units of one or more hidden layers of the action selection policy neural network.
• the feature control neural network may be associated with an auxiliary task reward for each unit of a particular hidden layer of the action selection policy neural network, and the system may determine the auxiliary task reward associated with a specific unit of the particular hidden layer as the difference between the activation of the unit generated during processing the observation at the time step and the activation of the unit generated during processing the observation at the next time step.
• the auxiliary control neural network processes the intermediate output of the action selection policy neural network to generate policy outputs (step 204).
• the auxiliary control neural network generates a policy output corresponding to each auxiliary task reward.
• the particular form of the policy outputs generated by the auxiliary control neural networks depends on the reinforcement learning technique used to train the auxiliary control neural network.
• the policy outputs generated by the auxiliary control neural network are, for each auxiliary task reward and for each possible action to be performed by the agent, an estimate of the long-term time-discounted auxiliary task reward if the agent performs the possible action in response to receiving the observation.
• the policy outputs may be an N act x n x n tensor Q, where N acC is the number of possible actions that can be performed by the agent and Qfajj) is an estimate of the long-term time-discounted change in the pixels in the (ij) th region of the n n non-overlapping grid placed over the observation image if the agent performs the action a in response to the input received by the pixel control neural network.
• the policy outputs may be an N act X m tensor Q, where m is the number of hidden units in a particular hidden layer of the action selection neural network, and Q(a,k) is an estimate of the long-term time-discounted change in the activations generated by the unit k if the agent performs the possible action a in response to the input received by the feature control neural network.
• the system backpropagates gradients that the system determines based on the auxiliary task reward and the policy output generated by the auxiliary control neural network for the auxiliary task reward, into the auxiliary control neural network and the action selection policy neural network (step 206).
• the system backpropagates gradients to maximize an expected long-term time- discounted auxiliary task reward that would be achieved by the system selecting actions in response to inputs in accordance with the policy output generated by the auxiliary control neural network corresponding to the auxiliary task reward.
• the gradients backpropagated by the sy stem depend on the particular choice of reinforcement learning technique used to train the auxiliary control neural network.
• the system uses an off-policy reinforcement learning technique to train the auxiliary control neural network, such as one-step or «-step Q- learning.
• the system uses an on-policy reinforcement learning technique to train the auxiliary control neural network, such as a reinforcement learning technique that learns value functions for each auxiliary task reward.
• the system may associate a weight factor to each auxiliary task reward, and the gradients that the system backpropagates based on the auxiliary task reward and the policy output for the auxiliary task reward may be scaled by the associated weight factor.
• the system adjusts the parameters of the action selection policy neural network corresponding to (i) the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network that the system provides as input to the auxiliary control neural network, and (ii) units that feed-forward into the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network that the system provides as input to the auxiliary control neural network.
• the process 200 for training the action selection neural network by training the auxiliary control neural network repeats at each of multiple time steps. Moreover, for a given time step, the process 200 may be repeated one or more times, for example by repeatedly sampling the replay memory.
• FIG. 3 is a flow diagram of an example process 300 for training the action selection policy neural network by training a reward prediction neural network.
• the process 300 will be described as being performed by a system of one or more computers located in one or more locations.
• a reinforcement learning system e.g., the reinforcement learning sy stem 100 of FIG. 1 , appropriately programmed in accordance with this specification, can perform the process 300.
• the system obtains experience tuple data from previous time steps in the replay memory, including observations for a sequence of previous time and the actual reward received with the observation following the last observation (step 301).
• the system samples sequences from the replay memory for which the actual reward received with the observation following the last observation in the sequence is non-zero with a higher probability than sequences for which the actual reward received with the observation following the last observation in the sequence is zero.
• the system may sample sequences so that the probability of sampling a sequence for which the actual reward received with the observation following the last observation in the sequence is non-zero with probability 0.5.
• the system processes the sequence of observations using the action selection policy neural network to generate one or more intermediate outputs that characterize the sequence of observations (step 302).
• the intermediate neural network of the action selection policy neural network is a recurrent neural network and the one or more intermediate outputs generated by the action selection policy neural network that characterize the sequence of observations are the intermediate representation generated by the recurrent neural network for the last observation in the sequence.
• the one or more intermediate outputs generated by the action selection policy neural network that characterize the sequence of observations are the encoded representations of the action selection policy neural network for the observations in the sequence.
• the system provides the one or more intermediate outputs generated by the action selection policy neural network that characterize the sequence of observations as input to the reward prediction neural network, and the reward prediction neural network processes the sequence of one or more intermediate outputs according to a set of reward prediction neural network parameters to generate as output a prediction for the reward received with the observation following the last observation (step 304).
• the system backpropagates gradients that the system determines based on the predicted reward generated by the reward prediction neural network into the reward prediction neural network and the action selection policy neural network (step 306).
• the system backpropagates gradients to minimize a loss function.
• the loss function is given by the mean-squared error between the actual reward received with the observation following the last observation in the sequence and the prediction for the reward received with the observation following the last observation in the sequence.
• the loss function is a multi-class cross-entropy classification loss, where the three classes are positive reward, negative reward, and zero reward.
• the system may scale the gradients that the system backpropagates based on the predicted reward generated by the reward prediction neural network by a weight factor.
• the system adjusts the parameters of the action selection policy neural network corresponding to (i) the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network that the system provides as input to the auxiliary control neural network, and (ii) units that feed-forward into the one or more units of the one or more hidden layers of the intermediate output of the action selection policy neural network that the system provides as input to the auxiliary control neural network.
• the process 300 for training the action selection neural network by training the reward prediction neural network repeats at each of multiple time steps. Moreover, for a given time step, the process 300 is repeated one or more times, by repeatedly sampling the replay memory.
• Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
• Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non-transitor storage medium for execution by, or to control the operation of, data processing apparatus.
• the computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a
• program instructions can be encoded on an artificially-generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus.
• an artificially-generated propagated signal e.g., a machine-generated electrical, optical, or electromagnetic signal
• data processing apparatus refers to data processing hardware
• the apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit).
• the apparatus can optionally include, in addition to hardware, code that creates an execution environment for computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.
• a computer program which may also be referred to or described as a program, software, a software application, an app, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages; and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing
• a program may, but need not, correspond to a file in a file system.
• a program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub-programs, or portions of code.
• a computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a data communication network.
• engine is used broadly to refer to a software-based system, subsystem, or process that is programmed to perform one or more specific functions.
• an engine will be implemented as one or more software modules or components, installed on one or more computers in one or more locations. In some cases, one or more computers will be dedicated to a particular engine; in other cases, multiple engines can be installed and running on the same computer or computers.
• the processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output.
• the processes and logic flows can also be performed by special purpose logic circuitry, e.g., an FPGA or an ASIC, or by a combination of special purpose logic circuitry and one or more programmed computers.
• Computers suitable for the execution of a computer program can be based on general or special purpose microprocessors or both, or any other kind of central processing unit.
• a central processing unit will receive instructions and data from a read-only memory or a random access memory or both.
• the essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data.
• the central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
• a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks.
• a computer need not have such devices.
• a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.
• PDA personal digital assistant
• GPS Global Positioning System
• USB universal serial bus
• Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory , media and memory devices, including by way of example semiconductor memory devices, e.g., EPRQM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and
• CD-ROM and D VD-ROM disks are CD-ROM and D VD-ROM disks.
• embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid cry stal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer.
• a display device e.g., a CRT (cathode ray tube) or LCD (liquid cry stal display) monitor
• a keyboard and a pointing device e.g., a mouse or a trackball
• Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.
• a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user's device in response to requests received from the web browser.
• a computer can interact with a user by sending text messages or other forms of message to a personal device, e.g., a smartphone that is running a messaging application, and receiving responsive messages from the user in return.
• Data processing apparatus for implementing machine learning models can also include, for example, special-purpose hardware accelerator units for processing common and compute- intensive parts of machine learning training or production, i.e., inference, workloads.
• Machine learning models can be implemented and deployed using a machine learning framework, e.g., a TensorFlow framework, a Microsoft Cognitive Toolkit framework, an Apache Singa framework, or an Apache MXNet framework.
• a machine learning framework e.g., a TensorFlow framework, a Microsoft Cognitive Toolkit framework, an Apache Singa framework, or an Apache MXNet framework.
• Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component e.g., a client computer having a graphical user interface, a web browser, or an app through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components.
• the components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (LAN) and a wide area network (WAN), e.g., the Internet.
• LAN local area network
• WAN wide area network
• the computing system can include clients and servers.
• a client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
• a server transmits data, e.g., an HTML page, to a user device, e.g., for purposes of displaying data to and receiving user input from a user interacting with the device, which acts as a client.
• Data generated at the user device e.g., a result of the user interaction, can be received at the server from the device.

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